1. Decimating Samples for Mesh Simplification

2. Surface Reconstruction
A sample and PL approximation

3. Sample Decimation Original 40K points = 0.33 12K points = 0.4

4. Local feature size and sampling
Medial axis
Local feature size f(p)
-sampling
  d(p)/f(p)

5. Voronoi structures

6. Cocones Space spanned by vectors making angle  /8 with horizontal
Compute cocones
Filter triangles whose duals intersect cocones
Extract manifold

7. Cocones, radius and height
cocones:C(p,,v) space by vectors making  /2 -  with a vector v.
radius r(p): radius of cocone
height h(p): min distance to the poles

8. Decimate

9. Cocone Lemma

10. Guarantees

11. Foot
 0.4
2046 points
Original
20021 points
 0.33
2714 points

12. Foot
 0.4
2046 points
 0.33
2714 points
 0.25
4116 points

13. Bunny
 0.4
7K points
 0.33
11K points
Original
35K points

14. Bunny
 0.4
7K points
 0.33
11K points
Original
35K points

15. Experimental Data

16. Conclusions
Introduced a measure radius/height ratio for skininess of Voronoi cells
We have used the radius/height ratio for sample decimation
Used it for boundary detection (SOCG01)
What about decimating supersize data (PVG01)
Can we use it to eliminate noise?
543,652 points
143 -> 28 min
3.5 million points
Unfin-> 198 min